# Pedestrian Localization with Stride-Wise Error Estimation and Compensation by Fusion of UWB and IMU Data

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

#### 2.1. NLOS Detection without Fusion

#### 2.2. Fusion under NLOS

## 3. Methods

#### 3.1. Virtual Stride Vector

#### 3.2. Error Models

#### 3.2.1. ZUPT Stride Vector

#### 3.2.2. Virtual Stride Vector—Length

#### 3.2.3. Virtual Stride Vector—Orientation

#### 3.2.4. Virtual Stride Vector—Translation

#### 3.3. Fusion of ZUPT and Virtual Stride Vector

#### 3.3.1. Orientation Filter

#### 3.3.2. Position Filter

## 4. Experiment

#### 4.1. Environments

#### 4.2. Ground Truth

^{2}halfway through a 20 m test section. Error influences remain due to user movements that do not precisely follow the given track; while these are partially compensated for by normalization, they cannot be quantified further.

## 5. Results

#### 5.1. Positioning Accuracy

#### 5.1.1. Dense LOS Environment

#### 5.1.2. Sparse LOS Environment

#### 5.1.3. Sparse NLOS Environment

#### 5.2. Attack Compensation

#### 5.2.1. Dense LOS Environment

#### 5.2.2. Sparse LOS Environment

#### 5.3. Conclusions

## 6. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

EKF | Extended Kalman Filter |

HDOP | Horizontal Dilution of Precision |

IMU | Inertial Measurement Unit |

KF | Kalman Filter |

LIDAR | Light Detection and Ranging |

LOS | Line Of Sight |

MAD | Mean Absolute Deviation |

NLOS | Non-Line of Sight |

PDR | Pedestrian Dead Reckoning |

UT | Unscented Transform |

UWB | Ultra-Wideband |

ZUPT | Zero Velocity Update |

## References

- Otim, T.; Bahillo, A.; Díez, L.E.; Lopez-Iturri, P.; Falcone, F. Impact of body wearable sensor positions on UWB ranging. IEEE Sens. J.
**2019**, 19, 11449–11457. [Google Scholar] [CrossRef] - Leu, P.; Camurati, G.; Heinrich, A.; Roeschlin, M.; Anliker, C.; Hollick, M.; Capkun, S.; Classen, J. Ghost Peak: Practical Distance Reduction Attacks Against {HRP}{UWB} Ranging. In Proceedings of the 31st USENIX Security Symposium (USENIX Security 22), Boston, MA, USA, 10–12 August 2022; pp. 1343–1359. [Google Scholar]
- Singh, M.; Roeschlin, M.; Zalzala, E.; Leu, P.; Čapkun, S. Security analysis of IEEE 802.15. 4z/HRP UWB time-of-flight distance measurement. In Proceedings of the 14th ACM Conference on Security and Privacy in Wireless and Mobile Networks, Abu Dhabi, United Arab Emirates, 28 June–2 July 2021; pp. 227–237. [Google Scholar]
- Botler, L.; Diwold, K.; Römer, K. A UWB-Based Solution to the Distance Enlargement Fraud Using Hybrid ToF and RSS Measurements. In Proceedings of the 2021 IEEE 18th International Conference on Mobile Ad Hoc and Smart Systems (MASS), Denver, CO, USA, 4–7 October 2021; pp. 324–334. [Google Scholar]
- Stocker, M.; Großwindhager, B.; Boano, C.A.; Römer, K. Towards secure and scalable UWB-based positioning systems. In Proceedings of the 2020 IEEE 17th International Conference on Mobile Ad Hoc and Sensor Systems (MASS), Delhi, India, 10–13 December 2020; pp. 247–255. [Google Scholar]
- Tiemann, J.; Friedrich, J.; Wietfeld, C. Experimental Evaluation of IEEE 802.15. 4z UWB Ranging Performance under Interference. Sensors
**2022**, 22, 1643. [Google Scholar] [CrossRef] [PubMed] - Carfano, G.; Murguia, H.; Gudem, P.; Mercier, P. Impact of FR1 5G NR jammers on UWB indoor position location systems. In Proceedings of the 2019 International Conference on Indoor Positioning and Indoor Navigation (IPIN), Pisa, Italy, 30 September–3 October 2019; pp. 1–8. [Google Scholar]
- Hou, X.; Bergmann, J. Pedestrian dead reckoning with wearable sensors: A systematic review. IEEE Sens. J.
**2020**, 21, 143–152. [Google Scholar] [CrossRef] - Kalman, R.E. A new approach to linear filtering and prediction problems. J. Basic Eng.
**1960**, 82, 35–45. [Google Scholar] [CrossRef] - Mehra, R. On the identification of variances and adaptive Kalman filtering. IEEE Trans. Autom. Control
**1970**, 15, 175–184. [Google Scholar] [CrossRef] - Dunik, J.; Straka, O.; Kost, O.; Havlik, J. Noise covariance matrices in state-space models: A survey and comparison of estimation methods—Part I. Int. J. Adapt. Control Signal Process.
**2017**, 31, 1505–1543. [Google Scholar] [CrossRef] - Najarro, L.A.C.; Song, I.; Kim, K. Fundamental Limitations and State-of-the-art Solutions for Target Node Localization in WSNs: A Review. IEEE Sens. J.
**2022**, 22, 23661–23682. [Google Scholar] [CrossRef] - Yao, L.; Yao, L.; Wu, Y.W. Analysis and Improvement of Indoor Positioning Accuracy for UWB Sensors. Sensors
**2021**, 21, 5731. [Google Scholar] [CrossRef] - Wu, S.; Li, J.; Liu, S. Single threshold optimization and a novel double threshold scheme for non-line-of-sight identification. Int. J. Commun. Syst.
**2014**, 27, 2156–2165. [Google Scholar] [CrossRef] - Wang, W.; Zeng, Z.; Ding, W.; Yu, H.; Rose, H. Concept and validation of a large-scale human-machine safety system based on real-time UWB indoor localization. In Proceedings of the 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Macau, China, 3–8 November 2019; pp. 201–207. [Google Scholar]
- Silva, B.; Hancke, G.P. Ranging error mitigation for through-the-wall non-line-of-sight conditions. IEEE Trans. Ind. Inform.
**2020**, 16, 6903–6911. [Google Scholar] [CrossRef] - Yu, K.; Wen, K.; Li, Y.; Zhang, S.; Zhang, K. A novel NLOS mitigation algorithm for UWB localization in harsh indoor environments. IEEE Trans. Veh. Technol.
**2018**, 68, 686–699. [Google Scholar] [CrossRef] - Dong, M. A low-cost NLOS identification and mitigation method for UWB ranging in static and dynamic environments. IEEE Commun. Lett.
**2021**, 25, 2420–2424. [Google Scholar] [CrossRef] - Yao, L.; Wu, Y.W.A.; Yao, L.; Liao, Z.Z. An integrated IMU and UWB sensor based indoor positioning system. In Proceedings of the 2017 International Conference on Indoor Positioning and Indoor Navigation (IPIN), Sapporo, Japan, 18–21 September 2017; pp. 1–8. [Google Scholar]
- Xia, M.; Xiu, C.; Yang, D.; Wang, L. A novel PDR aided UWB indoor positioning method. In Proceedings of the 2018 Ubiquitous Positioning, Indoor Navigation and Location-Based Services (UPINLBS), Wuhan, China, 22–23 March 2018; pp. 1–7. [Google Scholar]
- Naheem, K.; Kim, M.S. A low-cost foot-placed UWB and IMU fusion-based indoor pedestrian tracking system for IoT applications. Sensors
**2022**, 22, 8160. [Google Scholar] [CrossRef] [PubMed] - Long, K.; Shen, C.; Tian, C.; Zhang, K.; Bhatti, U.A.; Kong, D.F.N.; Feng, S.; Cheng, H. Single UWB anchor aided PDR heading and step length correcting indoor localization system. IEEE Access
**2021**, 9, 11511–11522. [Google Scholar] [CrossRef] - Zhang, Y.; Tan, X.; Zhao, C. UWB/INS integrated pedestrian positioning for robust indoor environments. IEEE Sens. J.
**2020**, 20, 14401–14409. [Google Scholar] [CrossRef] - Ali, R.; Liu, R.; Nayyar, A.; Qureshi, B.; Cao, Z. Tightly coupling fusion of UWB ranging and IMU pedestrian dead reckoning for indoor localization. IEEE Access
**2021**, 9, 164206–164222. [Google Scholar] [CrossRef] - Garcia, E.; Poudereux, P.; Hernandez, A.; Urena, J.; Gualda, D. A robust UWB indoor positioning system for highly complex environments. In Proceedings of the 2015 IEEE International Conference on Industrial Technology (ICIT), Seville, Spain, 17–19 March 2015; pp. 3386–3391. [Google Scholar]
- Tian, Q.; Kevin, I.; Wang, K.; Salcic, Z. An INS and UWB fusion approach with adaptive ranging error mitigation for pedestrian tracking. IEEE Sens. J.
**2020**, 20, 4372–4381. [Google Scholar] [CrossRef] - Barbieri, L.; Brambilla, M.; Trabattoni, A.; Mervic, S.; Nicoli, M. UWB localization in a smart factory: Augmentation methods and experimental assessment. IEEE Trans. Instrum. Meas.
**2021**, 70, 1–18. [Google Scholar] [CrossRef] - Zhu, J.; Kia, S.S. Bias compensation for UWB ranging for pedestrian geolocation applications. IEEE Sens. Lett.
**2019**, 3, 1–4. [Google Scholar] [CrossRef] - Novoselov, R.Y.; Herman, S.M.; Gadaleta, S.M.; Poore, A.B. Mitigating the effects of residual biases with Schmidt-Kalman filtering. In Proceedings of the 2005 7th International Conference on Information Fusion, Philadelphia, PA, USA, 25–28 July 2005; Volume 1. [Google Scholar]
- Simon, D. Kalman filtering with state constraints: A survey of linear and nonlinear algorithms. IET Control Theory Appl.
**2010**, 4, 1303–1318. [Google Scholar] [CrossRef] - Yang, G.; Zhu, S.; Li, Q.; Zhao, K. UWB/INS Based Indoor Positioning and NLOS Detection Algorithm for Firefighters. In Proceedings of the 2020 IEEE 22nd International Conference on High Performance Computing and Communications, IEEE 18th International Conference on Smart City, IEEE 6th International Conference on Data Science and Systems (HPCC/SmartCity/DSS), Yanuca Island, Fiji, 14–16 December 2020; pp. 909–916. [Google Scholar]
- Tong, H.; Xin, N.; Su, X.; Chen, T.; Wu, J. A robust pdr/uwb integrated indoor localization approach for pedestrians in harsh environments. Sensors
**2019**, 20, 193. [Google Scholar] [CrossRef] [PubMed] - Li, X.; Wang, Y.; Khoshelham, K. UWB/PDR tightly coupled navigation with robust extended Kalman filter for NLOS environments. Mob. Inform. Syst.
**2018**, 2018, 1–14. [Google Scholar] [CrossRef] - Chang, G. Robust Kalman filtering based on Mahalanobis distance as outlier judging criterion. J. Geod.
**2014**, 88, 391–401. [Google Scholar] [CrossRef] - Yang, X.; Wang, J.; Song, D.; Feng, B.; Ye, H. A novel NLOS error compensation method based IMU for UWB indoor positioning system. IEEE Sens. J.
**2021**, 21, 11203–11212. [Google Scholar] [CrossRef] - Liu, F.; Li, X.; Wang, J.; Zhang, J. An adaptive UWB/MEMS-IMU complementary kalman filter for indoor location in NLOS environment. Remote Sens.
**2019**, 11, 2628. [Google Scholar] [CrossRef] - Kim, D.H.; Pyun, J.Y. NLOS identification based UWB and PDR hybrid positioning system. IEEE Access
**2021**, 9, 102917–102929. [Google Scholar] [CrossRef] - Ferreira, A.G.; Fernandes, D.; Branco, S.; Catarino, A.P.; Monteiro, J.L. Feature selection for real-time NLOS identification and mitigation for body-mounted UWB transceivers. IEEE Trans. Instrum. Meas.
**2021**, 70, 1–10. [Google Scholar] [CrossRef] - Tian, Q.; Kevin, I.; Wang, K.; Salcic, Z. A resetting approach for INS and UWB sensor fusion using particle filter for pedestrian tracking. IEEE Trans. Instrum. Meas.
**2019**, 69, 5914–5921. [Google Scholar] [CrossRef] - Holzke, F.; Golatowski, F.; Timmermann, D. Stride Reconstruction Through Frequent Location Updates and Step Detection. In Proceedings of the 2022 IEEE International Workshop on Metrology for Industry 4.0 & IoT (MetroInd4. 0&IoT), Trento, Italy, 7–9 June 2022; pp. 212–217. [Google Scholar]
- Feliz Alonso, R.; Zalama Casanova, E.; Gomez Garcia-Bermejo, J. Pedestrian tracking using inertial sensors. J. Phys. Agents
**2009**, 3, 35–43. [Google Scholar] [CrossRef] - Holzke, F.; Wolff, J.P.; Golatowski, F.; Haubelt, C. Low-complexity online correction and calibration of pedestrian dead reckoning using map matching and GPS. Geo-Spat. Inf. Sci.
**2019**, 22, 114–127. [Google Scholar] [CrossRef] - Nilsson, J.O.; Skog, I.; Haendel, P. Performance characterisation of foot-mounted ZUPT-aided INSs and other related systems. In Proceedings of the 2010 International Conference on Indoor Positioning and Indoor Navigation, Zurich, Switzerland, 15–17 September 2010; pp. 1–7. [Google Scholar]
- Wang, Y.; Chernyshoff, A.; Shkel, A.M. Error analysis of ZUPT-aided pedestrian inertial navigation. In Proceedings of the 2018 International Conference on Indoor Positioning and Indoor Navigation (IPIN), Nantes, France, 24–27 September 2018; pp. 206–212. [Google Scholar]
- Wang, Y.; Chernyshoff, A.; Shkel, A.M. Study on estimation errors in ZUPT-aided pedestrian inertial navigation due to IMU noises. IEEE Trans. Aerosp. Electron. Syst.
**2019**, 56, 2280–2291. [Google Scholar] [CrossRef] - Saxena, K.L.; Alam, K. Estimation of the non-centrality parameter of a chi squared distribution. Ann. Stat.
**1982**, 10, 1012–1016. [Google Scholar] [CrossRef] - Mahan, R.P. Circular Statistical Methods: Applications in Spatial and Temporal Performance Analysis; US Army Research Institute for the Behavioral and Social Sciences: Alexandria, VA, USA, 1991; Volume 16. [Google Scholar]
- Julier, S.J.; Uhlmann, J.K. Consistent debiased method for converting between polar and Cartesian coordinate systems. Proc. Acquis. Track. Point. XI SPIE
**1997**, 3086, 110–121. [Google Scholar] - Villani, C. Optimal Transport: Old and New; Springer: Cham, Switzerland, 2009; Volume 338. [Google Scholar]
- Panaretos, V.M.; Zemel, Y. Statistical aspects of Wasserstein distances. Annu. Rev. Stat. Appl.
**2019**, 6, 405–431. [Google Scholar] [CrossRef] - Givens, C.R.; Shortt, R.M. A class of Wasserstein metrics for probability distributions. Mich. Math. J.
**1984**, 31, 231–240. [Google Scholar] [CrossRef] - Dowson, D.; Landau, B. The Frechet distance between multivariate normal distributions. J. Multivar. Anal.
**1982**, 12, 450–455. [Google Scholar] [CrossRef] - Murtagh, E.M.; Mair, J.L.; Aguiar, E.; Tudor-Locke, C.; Murphy, M.H. Outdoor walking speeds of apparently healthy adults: A systematic review and meta-analysis. Sport. Med.
**2021**, 51, 125–141. [Google Scholar] [CrossRef] - Hyndman, R.J.; Fan, Y. Sample quantiles in statistical packages. Am. Stat.
**1996**, 50, 361–365. [Google Scholar]

**Figure 1.**Error estimation and positioning fusion framework. The bold blocks are detailed separately in the following sections. Red elements are derived from IMU data, blue elements are derived from UWB data, and black elements are derived from combined IMU and UWB data. Here, $Var\left(X\right)$ is the variance of a random variable X, $Cov\left(X\right)$ is its covariance, a is the acceleration, $\omega $ is the turn rate, ${\varrho}^{Z}$ and $\Delta {\phi}^{Z}$ are the length and orientation change of the stride vector from ZUPT, respectively, ${\phi}^{Z}$ is the ZUPT vector orientation, ${\mathbf{\phi}}^{\mathit{Z}}$ is the set of ZUPT vector orientations, P is the UWB position measurement, ${\varrho}^{U}$ and ${\phi}^{U}$ are the length and orientation of the virtual stride vector from UWB, respectively, ${V}_{o}^{U}$ is the vector endpoint of the virtual stride vector from UWB, and $\widehat{\phi}$ is the filtered stride orientation.

**Figure 3.**Dense environment with high anchor density: (

**a**) test tracks and anchor placement (UWB BS) and (

**b**) HDOP. Please note that GT_L is placed on top of a section of GT_P.

**Figure 5.**Sparse LOS environment with low anchor density: (

**a**) test tracks and anchor placement (UWB BS) and (

**b**) HDOP. Please note that GT_L is placed on top of a section of GT_SQ.

**Figure 6.**Sparse NLOS environment with low anchor density and shadowing: (

**a**) test tracks and anchor placement (UWB BS); (

**b**) Sparse NLOS environment with low anchor density and shadowing. Large objects that can lead to NLOS are drawn in black. Please note that GT_L is placed on top of a section of GT_SQ.

**Figure 7.**The objects used to obscure the line of sight in the Sparse NLOS environment: (

**a**) start and end of test tracks with line of sight strongly obscured by vehicles and concrete pillars; (

**b**) large metallic object in the center of the test environment.

**Figure 8.**The numbered stride vectors from ZUPT on a straight track and a circuit over several straight subsections: (

**a**) straight line to and from, with clear transition between straight sections at stride 13; (

**b**) round trip with strides 16 and 24 without clear separation between even subsections. All graph axes are in meters.

**Figure 10.**Mean position error and standard deviation in the environment with high anchor density: (

**a**) straight track GT_L back and forth (

**b**) and roundtrip GT_P. All values are in meters.

**Figure 12.**Mean position error and standard deviation in the Sparse LOS test environment with low anchor density: (

**a**) straight track GT_L back and forth and (

**b**) roundtrip GT_SQ. All values are in meters.

**Figure 14.**Mean position error and standard deviation in the Sparse NLOS test environment with low anchor density: (

**a**) straight track GT_L back and forth (two tracks did not converge); (

**b**) roundtrip GT_SQ (five tracks did not converge). All values are in meters.

**Figure 16.**Mean position error of raw UWB and fused position on the GT_L track in the Dense environment. The data points show the mean accuracy for a certain bias direction. All values are in meters. One test run did not converge and was excluded from the analysis.

**Figure 17.**Mean position error of raw UWB and fused position on the GT_P track in the Dense environment. The data points show the mean accuracy for a certain bias direction. All values are in meters.

**Figure 18.**Mean position error of raw UWB and fused position on the GT_L track in the Sparse LOS environment. The data points show the mean accuracy for a certain bias direction. All values are in meters. One test run did not converge and was excluded from the analysis.

**Figure 19.**Mean position error of raw UWB and fused position on the GT_SQ track in the Sparse LOS environment. The data points show the mean accuracy for a certain bias direction. All values are in meters.

**Figure 20.**The GT_P track with two directions of simulated bias: (

**a**) bias vector ${(-1,0)}^{T}$ and (

**b**) bias vector ${(1,0)}^{T}$.

**Table 1.**The evaluated modes of the measurement update variance in the orientation and position filters.

Mode | Description |
---|---|

stat_10 | Static standard deviation of 0.05 rad & 0.1 m |

stat_20 | Static standard deviation of 0.1 rad & 0.2 m |

stat_30 | Static standard deviation of 0.15 rad & 0.3 m |

stat_40 | Static standard deviation of 0.2 rad & 0.4 m |

stat_50 | Static standard deviation of 0.25 rad & 0.5 m |

vec_5 | Dynamic variance by comparison of the last 5 strides |

vec_10 | Dynamic variance by comparison of the last 10 strides |

vec_15 | Dynamic variance by comparison of the last 15 strides |

**Table 2.**Mean position error (Avg), standard deviation (SD) and the percentage change of mean error compared to the UWB measurement (Avg vs. UWB) in the Dense environment. All values in meters.

Mode | Avg (SD) | Avg vs. UWB |
---|---|---|

(a) Straight track GT_L back and forth | ||

uwb | 0.2969 (0.0302) | 0.0000 |

uwb_vec | 0.2837 (0.0313) | −0.0444 |

stat_10 | 0.2931 (0.0645) | −0.0128 |

stat_20 | 0.2961 (0.0872) | −0.0028 |

stat_30 | 0.2950 (0.1010) | −0.0062 |

stat_40 | 0.2944 (0.1099) | −0.0084 |

stat_50 | 0.2946 (0.1160) | −0.0077 |

vec_5 | 0.2702 (0.0638) | −0.0898 |

vec_10 | 0.2656 (0.0633) | −0.1053 |

vec_15 | 0.2654 (0.0650) | −0.1060 |

(b) Roundtrip GT_P | ||

uwb | 0.3489 (0.0405) | 0.0000 |

uwb_vec | 0.3320 (0.0463) | −0.0482 |

stat_10 | 0.2904 (0.0725) | −0.1676 |

stat_20 | 0.2861 (0.0816) | −0.1801 |

stat_30 | 0.2897 (0.0832) | −0.1697 |

stat_40 | 0.2953 (0.0824) | −0.1535 |

stat_50 | 0.3008 (0.0817) | −0.1377 |

vec_5 | 0.2876 (0.0885) | −0.1757 |

vec_10 | 0.2910 (0.0893) | −0.1659 |

vec_15 | 0.2897 (0.0880) | −0.1695 |

**Table 3.**Mean position error (Avg), standard deviation (SD) and the percentage change of mean error compared to the UWB measurement (Avg vs. UWB) in the Sparse LOS environment. All values in meters.

Mode | Avg (SD) | Avg vs UWB |
---|---|---|

(a) Straight track GT_L back and forth | ||

uwb | 0.6078 (0.2370) | 0.0000 |

uwb_vec | 0.5592 (0.2187) | −0.0800 |

stat_10 | 0.6283 (0.2378) | 0.0337 |

stat_20 | 0.6487 (0.2242) | 0.0674 |

stat_30 | 0.6553 (0.2204) | 0.0782 |

stat_40 | 0.6606 (0.2198) | 0.0868 |

stat_50 | 0.6659 (0.2200) | 0.0956 |

vec_5 | 0.5966 (0.1983) | −0.0184 |

vec_10 | 0.5940 (0.1989) | −0.0227 |

vec_15 | 0.5948 (0.2014) | −0.0213 |

(b) Roundtrip GT_SQ | ||

uwb | 0.6364 (0.1861) | 0.0000 |

uwb_vec | 0.5916 (0.1787) | −0.0704 |

stat_10 | 0.5510 (0.1915) | −0.1343 |

stat_20 | 0.5585 (0.1954) | −0.1225 |

stat_30 | 0.5664 (0.1956) | −0.1100 |

stat_40 | 0.5712 (0.1948) | −0.1025 |

stat_50 | 0.5747 (0.1940) | −0.0970 |

vec_5 | 0.5684 (0.2214) | −0.1069 |

vec_10 | 0.5561 (0.2126) | −0.1263 |

vec_15 | 0.5451 (0.2091) | −0.1435 |

**Table 4.**Mean position error (Avg), standard deviation (SD) and the percentage change of mean error compared to the UWB measurement (Avg vs. UWB) in the Sparse NLOS environment. All values in meters.

Mode | Avg (SD) | Avg vs. UWB |
---|---|---|

(a) Straight track GT_L back and forth | ||

uwb | 1.7266 (0.5467) | 0.0000 |

uwb_vec | 1.7030 (0.5455) | −0.0137 |

stat_10 | 1.7208 (0.4982) | −0.0034 |

stat_20 | 1.6118 (0.5765) | −0.0665 |

stat_30 | 1.4387 (0.3568) | −0.1667 |

stat_40 | 1.4485 (0.3460) | −0.1611 |

stat_50 | 1.4630 (0.3435) | −0.1527 |

vec_5 | 1.0145 (0.3528) | −0.4125 |

vec_10 | 0.9659 (0.3408) | −0.4406 |

vec_15 | 0.9127 (0.3477) | −0.4714 |

(b) Roundtrip GT_SQ | ||

uwb | 1.7146 (0.5467) | 0.0000 |

uwb_vec | 1.6733 (0.5418) | −0.0241 |

stat_10 | 1.5586 (0.5611) | −0.0910 |

stat_20 | 1.5223 (0.6321) | −0.1121 |

stat_30 | 1.5101 (0.6916) | −0.1192 |

stat_40 | 1.5109 (0.7275) | −0.1188 |

stat_50 | 1.5129 (0.7499) | −0.1176 |

vec_5 | 1.2473 (0.4008) | −0.2725 |

vec_10 | 1.3066 (0.5701) | −0.2380 |

vec_15 | 1.3066 (0.6139) | −0.2380 |

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## Share and Cite

**MDPI and ACS Style**

Hölzke, F.; Borstell, H.; Golatowski, F.; Haubelt, C.
Pedestrian Localization with Stride-Wise Error Estimation and Compensation by Fusion of UWB and IMU Data. *Sensors* **2023**, *23*, 4744.
https://doi.org/10.3390/s23104744

**AMA Style**

Hölzke F, Borstell H, Golatowski F, Haubelt C.
Pedestrian Localization with Stride-Wise Error Estimation and Compensation by Fusion of UWB and IMU Data. *Sensors*. 2023; 23(10):4744.
https://doi.org/10.3390/s23104744

**Chicago/Turabian Style**

Hölzke, Fabian, Hagen Borstell, Frank Golatowski, and Christian Haubelt.
2023. "Pedestrian Localization with Stride-Wise Error Estimation and Compensation by Fusion of UWB and IMU Data" *Sensors* 23, no. 10: 4744.
https://doi.org/10.3390/s23104744